Question

Two circles touch each other externally at P. AB is a common tangent to the circles touching them at A and B. Find the value of CAP.​

Answer 1

Step-by-step explanation:

Given X and Y are two circles touch each other externally at P. AB is the common tangent to the circles X and Y at point A and B respectively.

let ∠CAP=α and ∠CBP=β.

CA = CP [lengths of the tangents from an external point C].

In a triangle PAC, ∠CAP=∠APC=α

Similarly CB = CP and ∠CPB=∠PBC=β

Now in the triangle APB,

∠PAB+∠PBA+∠APB=180

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[sum of the interior angles in a triangle]

α+β+(α+β)=180

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2α+2β=180

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α+β=90

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Thereofre, ∠APB=α+β=90

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